Shigeki Akiyama ; Franz Gähler ; Jeong-Yup Lee - Determining pure discrete spectrum for some self-affine tilings

dmtcs:2089 - Discrete Mathematics & Theoretical Computer Science, December 16, 2014, Vol. 16 no. 3 - https://doi.org/10.46298/dmtcs.2089
Determining pure discrete spectrum for some self-affine tilingsArticle

Authors: Shigeki Akiyama ORCID1; Franz Gähler 2; Jeong-Yup Lee 3

  • 1 Institute of Mathematics, University of Tsukuba
  • 2 Fakultät für Mathematik = Faculty of Mathematics [Bielefeld]
  • 3 Department of Mathematics Education [Kwandong]

By the algorithm implemented in the paper by Akiyama-Lee [Adv. Math. 226(4):2855 13;2883, 2011] and some of its predecessors, we have examined the pure discreteness of the spectrum for all irreducible Pisot substitutions of trace less than or equal to 2, and some cases of planar tilings generated by boundary substitutions due to Kenyon [Geom. Func. Anal. 6:471 13;488, 1996].

https://doi.org/10.46298/dmtcs.2089
Source: HAL:hal-01188903v1
Volume: Vol. 16 no. 3
Section: Discrete Algorithms
Published on: December 16, 2014
Submitted on: April 4, 2014
Keywords: Pisot substitution,pure discrete spectrum,self-affine tiling,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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